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Vibrations of a diatomic molecule are usually modelled by a harmonic potential. If the potential is given by X2, the correct statement is:
- a)F = 2x, K = 2
- b)F = –2x, K = 2
- c)F = 2x, K = –1
- d)F = –2x, K = –1
Correct answer is option 'B'. Can you explain this answer?
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Vibrations of a diatomic molecule are usually modelled by a harmonic p...
Understanding Harmonic Potential
In the context of molecular vibrations, a harmonic potential can be expressed mathematically as V(x) = kx², where V is the potential energy, x is the displacement from the equilibrium position, and k is the force constant.
Force Derivation
The force (F) acting on the molecule can be derived from the potential energy function using the relation:
F = -dV/dx.
For the given potential V(x) = x²:
- Differentiate V with respect to x:
- dV/dx = 2x.
- Thus, the force is:
- F = -dV/dx = -2x.
This indicates that the force acting on the molecule is proportional to the displacement, but in the opposite direction (restoring force).
Force Constant (K)
The force constant (k) in a harmonic oscillator is associated with how stiff the potential is:
- In a harmonic potential, k = 2 (from the coefficient of x² in V(x) = kx²).
- Therefore, K = 2 in this case.
Conclusion
Based on the above analysis:
- The correct expression for the force is:
- F = -2x (indicating a restoring force).
- The value of the force constant is:
- K = 2.
Thus, the correct answer is option 'B': F = -2x, K = 2. This aligns with the principles of harmonic motion in diatomic molecules, where the restoring force is always directed towards equilibrium.
In the context of molecular vibrations, a harmonic potential can be expressed mathematically as V(x) = kx², where V is the potential energy, x is the displacement from the equilibrium position, and k is the force constant.
Force Derivation
The force (F) acting on the molecule can be derived from the potential energy function using the relation:
F = -dV/dx.
For the given potential V(x) = x²:
- Differentiate V with respect to x:
- dV/dx = 2x.
- Thus, the force is:
- F = -dV/dx = -2x.
This indicates that the force acting on the molecule is proportional to the displacement, but in the opposite direction (restoring force).
Force Constant (K)
The force constant (k) in a harmonic oscillator is associated with how stiff the potential is:
- In a harmonic potential, k = 2 (from the coefficient of x² in V(x) = kx²).
- Therefore, K = 2 in this case.
Conclusion
Based on the above analysis:
- The correct expression for the force is:
- F = -2x (indicating a restoring force).
- The value of the force constant is:
- K = 2.
Thus, the correct answer is option 'B': F = -2x, K = 2. This aligns with the principles of harmonic motion in diatomic molecules, where the restoring force is always directed towards equilibrium.
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Vibrations of a diatomic molecule are usually modelled by a harmonic potential. If the potential is given by X2, the correct statement is:a)F = 2x, K = 2b)F = –2x, K = 2c)F = 2x, K = –1d)F = –2x, K = –1Correct answer is option 'B'. Can you explain this answer?
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Vibrations of a diatomic molecule are usually modelled by a harmonic potential. If the potential is given by X2, the correct statement is:a)F = 2x, K = 2b)F = –2x, K = 2c)F = 2x, K = –1d)F = –2x, K = –1Correct answer is option 'B'. Can you explain this answer? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about Vibrations of a diatomic molecule are usually modelled by a harmonic potential. If the potential is given by X2, the correct statement is:a)F = 2x, K = 2b)F = –2x, K = 2c)F = 2x, K = –1d)F = –2x, K = –1Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Vibrations of a diatomic molecule are usually modelled by a harmonic potential. If the potential is given by X2, the correct statement is:a)F = 2x, K = 2b)F = –2x, K = 2c)F = 2x, K = –1d)F = –2x, K = –1Correct answer is option 'B'. Can you explain this answer?.
Solutions for Vibrations of a diatomic molecule are usually modelled by a harmonic potential. If the potential is given by X2, the correct statement is:a)F = 2x, K = 2b)F = –2x, K = 2c)F = 2x, K = –1d)F = –2x, K = –1Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Chemistry.
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